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Topics in Intersection Graph Theory

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Topics in Intersection Graph Theory

Topics in Intersection Graph Theory

Terry A. McKee
F. R. McMorris
February 1999
Paperback
9780898714302
AUD$160.00
inc GST
Paperback
    Description

    Finally there is a book that presents real applications of graph theory in a unified format. This book is the only source for an extended, concentrated focus on the theory and techniques common to various types of intersection graphs. It is a concise treatment of the aspects of intersection graphs that interconnect many standard concepts and form the foundation of a surprising array of applications to biology, computing, psychology, matrices, and statistics.
    The authors emphasize the underlying tools and techniques and demonstrate how this approach constitutes a definite theory within graph theory. Some of the applications are not widely known or available in the graph theoretic literature and are presented here for the first time. The book also includes a detailed literature guide for many specialized and related areas, a current bibliography, and more than 100 exercises.

    Product details

    February 1999
    Paperback
    9780898714302
    213 pages
    250 × 178 × 11 mm
    0.384kg
    This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.

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    Contents

    Table of Contents

    • Preface
    • 1. Intersection Graphs. Basic Concepts
    • Intersection Classes
    • Parsimonious Set Representations
    • Clique Graphs
    • Line Graphs
    • Hypergraphs
    • 2. Chordal Graphs. Chordal Graphs as Intersection Graphs
    • Other Characterizations
    • Tree Hypergraphs
    • Some Applications of Chordal Graphs
    • Split Graphs
    • 3. Interval Graphs. Definitions and Characterizations
    • Interval Hypergraphs
    • Proper Interval Graphs
    • Some Applications of Interval Graphs
    • 4. Competition Graphs. Neighborhood Graphs
    • Competition Graphs
    • Interval Competition Graphs
    • Upper Bound Graphs
    • 5. Threshold Graphs. Definitions and Characterizations
    • Threshold Graphs as Intersection Graphs
    • Difference Graphs and Ferrers Digraphs
    • Some Applications of Threshold Graphs
    • 6. Other Kinds of Intersection. p-Intersection Graphs
    • Intersection Multigraphs and Pseudographs
    • Tolerance Intersection Graphs
    • 7. Guide to Related Topics. Assorted Geometric Intersection Graphs
    • Bipartite Intersection Graphs, Intersection Digraphs, and Catch (Di)Graphs
    • Chordal Bipartite and Weakly Chordal Graphs
    • Circle Graphs and Permutation Graphs
    • Clique Graphs of Chordal Graphs and Clique-Helly Graphs
    • Containment, Comparability, Cocomparability, and Asteroidal Triple-Free Graphs
    • Infinite Intersection Graphs
    • Miscellaneous Topics
    • P4-Free Chordal Graphs and Cographs
    • Powers of Intersection Graphs
    • Sphere-of-Influence Graphs
    • Strongly Chordal Graphs
    • Bibliography
    • Index.
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